Practice Set 1 – Solutions ചുറ്റളവും വ്യാസവും
Two questions that use only the big fact of the last page: circumference changes in the same proportion as diameter. No π yet – just scaling.
- Double the diameter (വ്യാസം) ⇒ double the circumference (ചുറ്റളവ്); half the diameter ⇒ half the circumference; 1½ times ⇒ 1½ times.
- A wire bent into a circle: its length is the circumference.
Question 1 · From one measured circle to others
വ്യാസം 2 മീറ്ററായ വൃത്തത്തിന്റെ ചുറ്റളവ് ഏകദേശം 6.28 മീറ്ററാണെന്ന് അളന്നു കണ്ടുപിടിച്ചു.
Q1. The circumference of a circle of diameter 2 metres was measured as about 6.28 metres. Without measuring, find the circumference of a circle of diameter (i) 4 m (ii) 1 m (iii) 3 m.
Compare each diameter with 2 m: how many times is it? The circumference is that many times 6.28 m.
(i) 4 m is twice 2 m ⇒ 2 × 6.28 = 12.56 m. (ii) 1 m is half of 2 m ⇒ ½ × 6.28 = 3.14 m. (iii) 3 m is 1½ times 2 m ⇒ 1½ × 6.28 = 9.42 m.
The circle of diameter 1 m has circumference about 3.14 m. Every other circumference is just 3.14 × diameter. That number is the star of the next page: π.
Question 2 · Half the wire
Q2. A wire is bent into a circle of diameter 4 cm. What will be the diameter of the circle made by bending a wire of half this length?
The wire length is the circumference. Half the circumference means half the diameter.
Half the wire ⇒ half the circumference ⇒ half the diameter: 2 cm.
A bangle maker who knows that 22 cm of gold wire makes a 7 cm bangle can say at once that 11 cm makes a 3.5 cm bangle for a child – no measuring tape needed.
Scale lab
Check yourself
- From one known circle (diameter 2 m, circumference 6.28 m) we get every other by scaling.
- Diameters 4, 1, 3 m ⇒ circumferences 12.56, 3.14, 9.42 m.
- Half the wire ⇒ half the diameter: 4 cm becomes 2 cm.
Next: π, a new number ▶